Year: 2011
Type: article
Abstract: We study the cones of pseudoeffective and nef cycles of higher codimension on the self product of an elliptic curve with complex multiplication, and on the product of a very general abelian surface with itself. In both cases, we find for instance the existence of nef classes that are not pseudoeffective, answering in the negative a question raised by Grothendieck in correspondence with Mumford. We also discuss several problems and questions for further investigation.
Source: Compositio Mathematica
Authors: Olivier Debarre, Lawrence Ein, Robert Lazarsfeld, Claire Voisin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2143068375